[ ^^i ] 



X^. X + ^ '■ 

 : X -^ 2, or of -7=:=^ — -rrj=r — =::r : X + X, will always be a ratio 

 ^— I. Jc+2. x + 6 



of greater inequality. 



I N the application of thefe fadors to the conftrudion of loga- 



ritnms - = ^ — ^— --j. _ , , which fradion (the above 



notation being ufed) when reduced to its loweft terms will have 

 unity for its numerator. For, of x and :v + 5, 2 always meafures 

 one, and 3 the other, as appears from what has been faid above ; 

 therefore 4 meafures the fquare of one ; and 9, the fquare of 

 the other (the quote of two fquare numbers being equal to the 

 fquare of the quote of their roots ; which laft is in this cafe an 

 integer) confequently 36 meafures the produd of their fquares 

 (the continual produd of any fadors being the fame, in what- 

 ever order the fadors be taken) and therefore it alfo meaiures 

 double that produd diminifhed by 36 ; i. e. 2. ;c'. ;7+5^" 36. 



Put the quote — -' ?_ -.T=jy; ~ will then be equal 



36 s ^ 



to — , by fubftitution of which the expreffion of the areneral fe- 



y 



ries will be rendered more fimple as before. 



The 



